Teutsche Algebra, Oder Algebraische Rechenkunst, zusamt ihrem Gebrauch: Bestehend 1. In Auflösung verworner Mathematischer Aufgaben. 2. In Verhandlung allerhand Algebraischer Æquationen. 3. In Erfindung unterschidlicher muzlicher Theorematum. Dem Teutschen Liebhaber Mathematischer Künsten nach einem neuen, und hiebevor niemalen im Trukk gesehenen Methodo zugefallen also verfasset.. by RAHN, Johann Heinrich, Landvogt zu Kyburg

Four folding printed tables & numerous woodcut diagrams in the text. 6 p.l. (two of these preliminary leaves are mis-bound at end), 188 pp., 4 leaves of errata at end. Small 4to, attractive antique calf, panelled in gilt, gilt fleurons in each corner, spine gilt. Zurich: J.J. Bodmer, 1659. First edition and an absolutely complete copy of this rare and noteworthy mathematical book; our copy has all four folding printed tables (most copies described in OCLC seem to have only three) and an extra leaf of errata not present in the Macclesfield copy (sale, Sotheby's London, 25 Oct. 2005, lot 1705, £12,000 including premium). In this book on page 73, Rahn first introduced the symbol "÷" in print "as a sign of division; (2) the Archimedean spiral for involution; (3) the double epsilon for evolution; (4) the use of capital letters B, D, E, for given numbers, and small letters a, b, for unknown numbers; (5) the * for multiplication; (6) the first use of ∴ for 'therefore'; (7) the three-column arrangement of which the left column contains the directions, the middle the numbers of the lines, the right the results of the operations."-Cajori, A History of Mathematical Notations, I, pp. 211-12 & see illus. on p. 213 (& see sections 205, 208, 232, 237, 266, 304, 307, 328, 333, 341, 385, & 386 for Rahn's other contributions, all of which appear in the present book). We know that Leibniz looked upon Rahn's book favorably, describing it as "an elegant algebra." While Rahn's use of the modern division sign was not immediately adopted in Europe, in England it met a very favorable reception, with John Wallis and other English writers employing it. Rahn (1622-76), came from a prominent Zurich family and had a major role in the administration of his native city. About 1654, Rahn came to know John Pell (1611-85), then a representative of the Commonwealth at Zurich, and engaged the English mathematician as a tutor in 1657, meeting every Friday night. While some of the advances in notation in this book might have derived from Pell, "without further evidence, it is best to assume that there was joint responsibility for these innovations and that Pell's contemporary reputation as a mathematician, and particularly as an algebraist, was not unearned."-D.S.B., X, p. 495. Fine crisp copy. Old library stamp on title. ❧ Cajori, A History of Mathematics, p. 140. Smith, History of Mathematics, I, p. 412 & II, pp. 406, 411-12, 431n, & 474. For Pell and his relationship with Rahn, see D.S.B., X, pp. 495-96.